FIA - NLS Models: Biomass Growth vs. Biomass, Temporally-balanced
JAH
2022-10-25
Background
This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince
Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(G\) with increasing \(B\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.
Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:
model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)
sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
NOTE:
This document contains a temporally balanced set of \(G\) observations. First, the data set limited to plots that meet our plot-based filtering criteria (see below). Then the data set was further restricted to plots with at least 2 \(G\) observations (i.e., three FIA tree census records), with one in each of the two following decades: 2000-2010 (including censuses part of FIA 3.0 from 1996-2000 as part of the 2000 panel), and 2011-2022. For plots that had >2 \(G\) observations we took the first and last ones.
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1677 observations.
Below the model fitting procedure is implemented by ecoprovince:
Temporally-balancing the biomass growth data set
Lets look at some quick attributes of the dataset:
- The data set has 104986 observations, comprised of 55492 plots.
- The frequency of growth measurements among plots is as follows : 25149, 13819, 13897, 2627.
- Thus 54.68 % of plots have at least two growth intervals.
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4772 3408.2
## 2 4771 3405.7 1 2.487 3.4837 0.06204 .
## 3 4770 3236.8 1 168.924 248.9422 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17319.61
## 2 2 17318.13
## 3 3 17077.21##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.139845 0.161516 0.866 0.387
## phi 0.006338 0.004974 1.274 0.203
## alpha 0.617108 0.036755 16.790 <2e-16 ***
## A 3.642778 0.116441 31.284 <2e-16 ***
## k 9.993586 0.836456 11.948 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8238 on 4770 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.089e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4770 3236.8
## 2 4769 3230.7 1 6.0211 8.8879 0.002885 **
## 3 4769 3231.1 0 0.0000
## 4 4768 3230.6 1 0.5307 0.7832 0.376203
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17077.21
## 2 3a 17070.32
## 3 3b 17070.93
## 4 3c 17072.14##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.144797 0.161620 0.896 0.370346
## phi 0.005887 0.004966 1.185 0.235888
## alpha 0.614851 0.036732 16.739 < 2e-16 ***
## A 3.724218 0.125492 29.677 < 2e-16 ***
## k 16.260444 3.008359 5.405 6.79e-08 ***
## p 0.197628 0.056420 3.503 0.000465 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8231 on 4769 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 5.737e-07
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9672, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -14.071, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1050 row(s) containing missing values (geom_path).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11685 9455.5
## 2 11682 9416.9 3 38.62 15.97 2.333e-10 ***
## 3 11681 8761.0 1 655.85 874.44 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 40222.79
## 2 2 40171.87
## 3 3 39330.25##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.554938 0.141202 3.930 8.54e-05 ***
## phi 0.026295 0.003682 7.142 9.72e-13 ***
## alpha 0.829228 0.025725 32.235 < 2e-16 ***
## A 2.959101 0.077541 38.162 < 2e-16 ***
## k 14.496808 0.635461 22.813 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.866 on 11681 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.138e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11681 8761.0
## 2 11680 8663.0 1 97.989 132.115 < 2.2e-16 ***
## 3 11680 8686.7 0 0.000
## 4 11679 8662.8 1 23.906 32.229 1.403e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 39330.25
## 2 3a 39200.81
## 3 3b 39232.70
## 4 3c 39202.49##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.541180 0.139710 3.874 0.000108 ***
## phi 0.026504 0.003654 7.254 4.31e-13 ***
## alpha 0.819098 0.025587 32.013 < 2e-16 ***
## A 3.212284 0.092789 34.619 < 2e-16 ***
## k 30.206408 2.545767 11.865 < 2e-16 ***
## p 0.188297 0.013330 14.126 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8612 on 11680 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 4.164e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1031 row(s) containing missing values (geom_path).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5341 5688.8
## 2 5340 5688.7 1 0.072 0.0674 0.7952
## 3 5339 5460.2 1 228.449 223.3761 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 22327.72
## 2 2 22329.65
## 3 3 22112.62##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.3566162 0.0943389 -14.380 <2e-16 ***
## phi -0.0003043 0.0053930 -0.056 0.955
## alpha 0.6601464 0.0417385 15.816 <2e-16 ***
## A 6.2586687 0.1870844 33.454 <2e-16 ***
## k 20.8894391 2.0689590 10.097 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.011 on 5339 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.62e-06
## (6 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5339 5460.2
## 2 5338 5413.6 1 46.661 46.01 1.304e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 22112.62
## 2 3a 22068.76
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.383e+00 9.279e-02 -14.906 < 2e-16 ***
## phi 1.158e-04 5.368e-03 0.022 0.983
## alpha 6.595e-01 4.125e-02 15.989 < 2e-16 ***
## A 7.706e+00 4.701e-01 16.392 < 2e-16 ***
## k 1.101e+02 2.780e+01 3.960 7.58e-05 ***
## p 3.385e-01 2.446e-02 13.837 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.007 on 5338 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 8.604e-06
## (6 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 5 rows containing missing values (geom_point).## Warning: Removed 1036 row(s) containing missing values (geom_path).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3242 2626.1
## 2 3241 2621.0 1 5.045 6.2389 0.01255 *
## 3 3240 2415.5 1 205.472 275.6030 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 11966.08
## 2 2 11961.84
## 3 3 11698.93##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.139424 0.216948 -0.643 0.5205
## phi 0.023646 0.009365 2.525 0.0116 *
## alpha 0.826107 0.045276 18.246 <2e-16 ***
## A 4.746405 0.209613 22.644 <2e-16 ***
## k 32.364828 2.388594 13.550 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8634 on 3240 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.622e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3240 2415.5
## 2 3239 2355.4 1 60.127 82.683 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 11698.93
## 2 3a 11619.13
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.172399 0.211318 -0.816 0.4147
## phi 0.021007 0.009159 2.294 0.0219 *
## alpha 0.818058 0.044729 18.289 < 2e-16 ***
## A 6.400734 0.440119 14.543 < 2e-16 ***
## k 117.199700 18.633196 6.290 3.6e-10 ***
## p 0.175050 0.012112 14.453 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8528 on 3239 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.67e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95574, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.702, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 2 rows containing missing values (geom_point).## Warning: Removed 1108 row(s) containing missing values (geom_path).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6041 5944.5
## 2 6040 5937.2 1 7.30 7.4261 0.006447 **
## 3 6039 5759.7 1 177.55 186.1577 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 23796.36
## 2 2 23790.93
## 3 3 23609.43##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.282209 0.095635 -13.407 <2e-16 ***
## phi -0.018755 0.006927 -2.707 0.0068 **
## alpha 0.629953 0.043517 14.476 <2e-16 ***
## A 6.705014 0.227860 29.426 <2e-16 ***
## k 47.968739 3.668489 13.076 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9766 on 6039 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 8.873e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 3 23609.43
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.282209 0.095635 -13.407 <2e-16 ***
## phi -0.018755 0.006927 -2.707 0.0068 **
## alpha 0.629953 0.043517 14.476 <2e-16 ***
## A 6.705014 0.227860 29.426 <2e-16 ***
## k 47.968739 3.668489 13.076 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9766 on 6039 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 8.873e-06
## (2 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 1 rows containing missing values (geom_point).## Warning: Removed 1145 row(s) containing missing values (geom_path).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7528 13282
## 2 7527 13280 1 1.3 0.7363 0.3909
## 3 7526 11939 1 1341.4 845.5545 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 37078.46
## 2 2 37079.73
## 3 3 36279.86##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.349482 0.105426 -3.315 0.000921 ***
## phi -0.009491 0.005218 -1.819 0.068961 .
## alpha 0.856907 0.026946 31.800 < 2e-16 ***
## A 5.817495 0.138279 42.071 < 2e-16 ***
## k 3.472531 0.361833 9.597 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.26 on 7526 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.303e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7526 11939
## 2 7525 11887 1 52.526 33.2522 8.415e-09 ***
## 3 7525 11886 0 0.000
## 4 7524 11885 1 1.393 0.8819 0.3477
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 36279.86
## 2 3a 36248.65
## 3 3b 36248.43
## 4 3c 36249.54##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.379037 0.104055 -3.643 0.000272 ***
## phi -0.009317 0.005197 -1.793 0.073059 .
## alpha 0.854135 0.026807 31.862 < 2e-16 ***
## A 6.816954 0.438500 15.546 < 2e-16 ***
## k 3.410291 0.872216 3.910 9.31e-05 ***
## s 0.464466 0.078786 5.895 3.90e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.257 on 7525 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.449e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1017 row(s) containing missing values (geom_path).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7564 16078
## 2 7563 16077 1 1.0 0.4711 0.4925
## 3 7562 14784 1 1293.7 661.7408 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 37504.72
## 2 2 37506.25
## 3 3 36873.46##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.290227 0.130592 -2.222 0.0263 *
## phi -0.012769 0.005708 -2.237 0.0253 *
## alpha 0.847614 0.029809 28.435 <2e-16 ***
## A 5.613649 0.169380 33.142 <2e-16 ***
## k 9.756220 0.724398 13.468 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.398 on 7562 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.119e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7562 14784
## 2 7561 14633 1 150.558 77.794 < 2.2e-16 ***
## 3 7561 14672 0 0.000
## 4 7560 14630 1 41.445 21.416 3.759e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 36873.46
## 2 3a 36798.00
## 3 3b 36818.10
## 4 3c 36798.69##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.299719 0.129141 -2.321 0.0203 *
## phi -0.013278 0.005661 -2.345 0.0190 *
## alpha 0.839169 0.029556 28.392 < 2e-16 ***
## A 6.046706 0.206060 29.344 < 2e-16 ***
## k 27.065470 4.019008 6.734 1.77e-11 ***
## p 0.283510 0.025089 11.300 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.391 on 7561 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.725e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 981 row(s) containing missing values (geom_path).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 780 1659.4
## 2 779 1659.4 1 0.058 0.0273 0.8687
## 3 778 1553.0 1 106.333 53.2677 7.195e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3854.426
## 2 2 3856.398
## 3 3 3806.544##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.3940896 0.8275950 0.476 0.63408
## phi -0.0009407 0.0260228 -0.036 0.97117
## alpha 0.8166398 0.1004937 8.126 1.74e-15 ***
## A 4.4837908 0.7184812 6.241 7.15e-10 ***
## k 10.4572437 3.2639381 3.204 0.00141 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.413 on 778 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.01e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234, :
## parameters without starting value in 'data': p
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 778 1553.0
## 2 777 1549.6 1 3.4384 1.7241 0.1896
## model AIC
## 1 3 3806.544
## 2 3a 3806.808
## 3 3b 3807.724
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.3940896 0.8275950 0.476 0.63408
## phi -0.0009407 0.0260228 -0.036 0.97117
## alpha 0.8166398 0.1004937 8.126 1.74e-15 ***
## A 4.4837908 0.7184812 6.241 7.15e-10 ***
## k 10.4572437 3.2639381 3.204 0.00141 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.413 on 778 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.01e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96129, p-value = 1.584e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.8967, p-value = 9.752e-05
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1077 row(s) containing missing values (geom_path).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1244 1027.5
## 2 1243 1025.3 1 2.2019 2.6694 0.1025447
## 3 1242 1015.6 1 9.7198 11.8868 0.0005842 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4525.811
## 2 2 4525.136
## 3 3 4515.258##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.77575 0.28728 -2.700 0.007021 **
## phi 0.01703 0.01283 1.327 0.184685
## alpha 0.38784 0.10800 3.591 0.000342 ***
## A 4.24498 0.31468 13.490 < 2e-16 ***
## k 23.59203 3.99166 5.910 4.41e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9043 on 1242 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.267e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1242 1015.58
## 2 1241 976.15 1 39.423 50.119 2.415e-12 ***
## 3 1240 974.33 1 1.821 2.317 0.1282
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 4515.258
## 2 3a 4467.887
## 3 3b NA
## 4 3c 4467.559##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.84078 0.27177 -3.094 0.002021 **
## phi 0.01821 0.01256 1.449 0.147540
## alpha 0.39633 0.10417 3.805 0.000149 ***
## A 5.45365 1.61675 3.373 0.000766 ***
## k 146.78996 71.07378 2.065 0.039100 *
## s 2.15122 1.02725 2.094 0.036449 *
## p 0.45332 0.15315 2.960 0.003136 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8864 on 1240 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 8.354e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93154, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.4546, p-value = 1.085e-10
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1176 row(s) containing missing values (geom_path).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 39 89.982
## 2 38 89.834 1 0.1482 0.0627 0.8037
## 3 37 85.256 1 4.5777 1.9867 0.1670
## model AIC
## 1 1 193.9007
## 2 2 195.8314
## 3 3 195.6347##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.5933 10.6637 0.431 0.669
## A 0.7165 0.9102 0.787 0.436
## k -24.0560 14.7537 -1.631 0.111
##
## Residual standard error: 1.519 on 39 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.243e-06
## (368 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 39 89.982
## 2 38 89.738 1 0.24349 0.1031 0.7499
## model AIC
## 1 1 193.9007
## 2 1a 195.7869
## 3 1b NA
## 4 1c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.5933 10.6637 0.431 0.669
## A 0.7165 0.9102 0.787 0.436
## k -24.0560 14.7537 -1.631 0.111
##
## Residual standard error: 1.519 on 39 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.243e-06
## (368 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96947, p-value = 0.3169
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.2014, p-value = 0.2296
## alternative hypothesis: two.sidedpredict and plot
## [1] "cannot plot data with prediction"plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start, :
## missing or negative weights not allowed
## Error in nls(fg_2, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## missing or negative weights not allowed
## Error in nls(fg_3, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## missing or negative weights not allowed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 127 112.40
## 2 126 112.13 1 0.26844 0.3016 0.5838
## 3 125 109.08 1 3.04756 3.4922 0.0640 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 421.2904
## 2 2 422.9796
## 3 3 421.3975##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2726 1.7336 0.157 0.8753
## A 4.1582 1.7879 2.326 0.0216 *
## k 101.1654 45.1400 2.241 0.0268 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9408 on 127 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.017e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 127 112.4
## 2 126 111.9 1 0.5007 0.5638 0.4541
## model AIC
## 1 1 421.2904
## 2 1a 422.7100
## 3 1b 423.2902
## 4 1c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2726 1.7336 0.157 0.8753
## A 4.1582 1.7879 2.326 0.0216 *
## k 101.1654 45.1400 2.241 0.0268 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9408 on 127 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.017e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87973, p-value = 7.476e-09
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.3275, p-value = 0.01994
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1140 row(s) containing missing values (geom_path).
plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
## Error in nls(fg_1, data = G_342, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
411 - Everglades
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5065 3432.2
## 2 5064 3422.9 1 9.366 13.857 0.0001994 ***
## 3 5063 3203.5 1 219.410 346.772 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18094.74
## 2 2 18082.89
## 3 3 17749.14##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.761618 0.197780 3.851 0.000119 ***
## phi 0.009659 0.004543 2.126 0.033552 *
## alpha 0.637881 0.031901 19.996 < 2e-16 ***
## A 2.976393 0.110283 26.989 < 2e-16 ***
## k 3.772365 0.519549 7.261 4.43e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7954 on 5063 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.116e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5063 3203.5
## 2 5062 3198.9 1 4.5233 7.1577 0.007489 **
## 3 5062 3201.7 0 0.0000
## 4 5061 3196.5 1 5.1833 8.2067 0.004191 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17749.14
## 2 3a 17743.98
## 3 3b 17748.33
## 4 3c 17742.12##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.764624 0.197840 3.865 0.000113 ***
## phi 0.009785 0.004551 2.150 0.031592 *
## alpha 0.639624 0.031815 20.105 < 2e-16 ***
## A 2.920474 0.110104 26.525 < 2e-16 ***
## k 16.710125 3.563713 4.689 2.82e-06 ***
## p 0.550821 0.067920 8.110 6.31e-16 ***
## s 1.963671 0.527659 3.721 0.000200 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7947 on 5061 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 7.106e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1108 row(s) containing missing values (geom_path).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5101 7235.7
## 2 5100 7226.6 1 9.07 6.401 0.01144 *
## 3 5099 7038.3 1 188.33 136.440 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 23011.44
## 2 2 23007.04
## 3 3 22874.26##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.717099 0.128899 -5.563 2.78e-08 ***
## phi -0.014903 0.007147 -2.085 0.0371 *
## alpha 0.731390 0.059496 12.293 < 2e-16 ***
## A 5.103329 0.170541 29.924 < 2e-16 ***
## k 11.127486 1.834527 6.066 1.41e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.175 on 5099 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.583e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5099 7038.3
## 2 5098 6977.9 1 60.345 44.088 3.467e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 22874.26
## 2 3a 22832.31
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -7.976e-01 1.244e-01 -6.413 1.56e-10 ***
## phi -1.168e-02 7.119e-03 -1.640 0.101
## alpha 7.273e-01 5.855e-02 12.422 < 2e-16 ***
## A 1.970e+01 2.772e+01 0.711 0.477
## k 1.969e+03 3.923e+03 0.502 0.616
## p 1.847e-01 2.532e-01 0.729 0.466
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.17 on 5098 degrees of freedom
##
## Number of iterations to convergence: 24
## Achieved convergence tolerance: 8.167e-07summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 982 row(s) containing missing values (geom_path).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 593 787.36
## 2 592 787.31 1 0.048 0.0361 0.8494
## 3 591 765.62 1 21.688 16.7417 4.878e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2418.067
## 2 2 2420.030
## 3 3 2405.382##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.232485 1.433829 1.557 0.1200
## phi -0.008071 0.030152 -0.268 0.7890
## alpha 0.855111 0.194706 4.392 1.33e-05 ***
## A 2.205356 0.463706 4.756 2.48e-06 ***
## k 16.759312 8.138542 2.059 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.138 on 591 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 8.07e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 2405.382
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.232485 1.433829 1.557 0.1200
## phi -0.008071 0.030152 -0.268 0.7890
## alpha 0.855111 0.194706 4.392 1.33e-05 ***
## A 2.205356 0.463706 4.756 2.48e-06 ***
## k 16.759312 8.138542 2.059 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.138 on 591 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 8.07e-06summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95527, p-value = 1.794e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.07064, p-value = 0.9437
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1175 row(s) containing missing values (geom_path).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 663 866.92
## 2 662 854.80 1 12.120 9.3866 0.002275 **
## 3 661 829.09 1 25.702 20.4908 7.107e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2729.245
## 2 2 2721.868
## 3 3 2703.536##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.10198 1.56501 1.343 0.17970
## phi 0.06479 0.02892 2.241 0.02539 *
## alpha 0.80384 0.16677 4.820 1.78e-06 ***
## A 2.13854 0.49961 4.280 2.14e-05 ***
## k 9.61180 3.71444 2.588 0.00987 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.12 on 661 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 9.664e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 2703.536
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.10198 1.56501 1.343 0.17970
## phi 0.06479 0.02892 2.241 0.02539 *
## alpha 0.80384 0.16677 4.820 1.78e-06 ***
## A 2.13854 0.49961 4.280 2.14e-05 ***
## k 9.61180 3.71444 2.588 0.00987 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.12 on 661 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 9.664e-06
## (2 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94157, p-value = 1.62e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.1287, p-value = 2.917e-07
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1218 row(s) containing missing values (geom_path).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 287 232.72
## 2 286 231.62 1 1.0968 1.3543 0.2455
## 3 285 212.75 1 18.8736 25.2837 8.764e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 815.8920
## 2 2 816.5219
## 3 3 793.8725##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.96003 1.22657 -0.783 0.43446
## phi 0.04116 0.03686 1.117 0.26507
## alpha 0.79777 0.13886 5.745 2.36e-08 ***
## A 3.07601 1.00185 3.070 0.00234 **
## k 37.38699 12.17334 3.071 0.00234 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.864 on 285 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.451e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 285 212.75
## 2 284 212.69 1 0.05782 0.0772 0.7813
## 3 284 212.73 0 0.00000
## 4 283 211.84 1 0.88809 1.1864 0.2770
## model AIC
## 1 3 793.8725
## 2 3a 795.7937
## 3 3b 795.8481
## 4 3c 796.6349##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.96003 1.22657 -0.783 0.43446
## phi 0.04116 0.03686 1.117 0.26507
## alpha 0.79777 0.13886 5.745 2.36e-08 ***
## A 3.07601 1.00185 3.070 0.00234 **
## k 37.38699 12.17334 3.071 0.00234 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.864 on 285 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.451e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91999, p-value = 2.424e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.4932, p-value = 0.1354
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1264 row(s) containing missing values (geom_path).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3a |
| 212 | Laurentian Mixed Forest | 3a |
| 221 | Eastern Broadleaf Forest | 3a |
| 222 | Midwest Broadleaf Forest | 3a |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3b |
| 232 | Outer Coastal Plain Mixed Forest | 3a |
| 234 | Lower Mississippi Riverine Forest | 3 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 3c |
| 255 | Prairie Parkland (Subtropical) | 1 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | 1 |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3c |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3a |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3 |
| M242 | Cascade Mixed Forest | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 4776 | 2388 | 0.1447972 | -0.1720528 | 0.4616472 | 0.0058868 | -0.0038484 | 0.0156220 | 0.6148505 | 0.5428383 | 0.6868628 | 3.724218 | 3.478196 | 3.970240 | 16.260444 | 10.3626711 | 22.158217 |
| 212 | Laurentian Mixed Forest | east | 11688 | 5844 | 0.5411803 | 0.2673246 | 0.8150360 | 0.0265039 | 0.0193417 | 0.0336661 | 0.8190979 | 0.7689440 | 0.8692519 | 3.212284 | 3.030402 | 3.394166 | 30.206408 | 25.2162797 | 35.196537 |
| 221 | Eastern Broadleaf Forest | east | 5350 | 2675 | -1.3830516 | -1.5649539 | -1.2011492 | 0.0001158 | -0.0104083 | 0.0106400 | 0.6594941 | 0.5786316 | 0.7403566 | 7.705926 | 6.784309 | 8.627543 | 110.104493 | 55.6037406 | 164.605245 |
| 222 | Midwest Broadleaf Forest | east | 3248 | 1624 | -0.1723992 | -0.5867296 | 0.2419312 | 0.0210067 | 0.0030495 | 0.0389639 | 0.8180581 | 0.7303573 | 0.9057588 | 6.400734 | 5.537794 | 7.263673 | 117.199700 | 80.6656540 | 153.733746 |
| 223 | Central Interior Broadleaf Forest | east | 6046 | 3023 | -1.2822090 | -1.4696880 | -1.0947301 | -0.0187547 | -0.0323341 | -0.0051753 | 0.6299529 | 0.5446443 | 0.7152614 | 6.705014 | 6.258327 | 7.151700 | 47.968739 | 40.7771918 | 55.160286 |
| 231 | Southeastern Mixed Forest | east | 7532 | 3766 | -0.3790368 | -0.5830140 | -0.1750597 | -0.0093167 | -0.0195043 | 0.0008708 | 0.8541345 | 0.8015847 | 0.9066843 | 6.816954 | 5.957372 | 7.676536 | 3.410291 | 1.7005048 | 5.120077 |
| 232 | Outer Coastal Plain Mixed Forest | east | 7568 | 3784 | -0.2997192 | -0.5528716 | -0.0465668 | -0.0132776 | -0.0243746 | -0.0021806 | 0.8391689 | 0.7812309 | 0.8971070 | 6.046706 | 5.642770 | 6.450642 | 27.065470 | 19.1870985 | 34.943842 |
| 234 | Lower Mississippi Riverine Forest | east | 784 | 392 | 0.3940896 | -1.2304942 | 2.0186735 | -0.0009407 | -0.0520240 | 0.0501425 | 0.8166398 | 0.6193690 | 1.0139107 | 4.483791 | 3.073399 | 5.894182 | 10.457244 | 4.0500748 | 16.864413 |
| 242 | Pacific Lowland Mixed Forest | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1248 | 624 | -0.8407789 | -1.3739527 | -0.3076051 | 0.0182077 | -0.0064416 | 0.0428570 | 0.3963256 | 0.1919630 | 0.6006881 | 5.453648 | 2.281780 | 8.625517 | 146.789957 | 7.3518120 | 286.228102 |
| 255 | Prairie Parkland (Subtropical) | pacific | 410 | 205 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 104 | 52 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 132 | 66 | 0.2725824 | -3.1578627 | 3.7030275 | NA | NA | NA | NA | NA | NA | 4.158174 | 0.620298 | 7.696051 | 101.165354 | 11.8414505 | 190.489258 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 2 | 1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 64 | 32 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 5068 | 2534 | 0.7646237 | 0.3767708 | 1.1524767 | 0.0097851 | 0.0008633 | 0.0187070 | 0.6396243 | 0.5772539 | 0.7019947 | 2.920474 | 2.704623 | 3.136325 | 16.710125 | 9.7237058 | 23.696544 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 5104 | 2552 | -0.7976484 | -1.0414924 | -0.5538044 | -0.0116772 | -0.0256335 | 0.0022792 | 0.7272817 | 0.6125057 | 0.8420577 | 19.701104 | -34.642618 | 74.044826 | 1968.521244 | -5722.3479658 | 9659.390454 |
| M223 | Ozark Broadleaf Forest Meadow | east | 596 | 298 | 2.2324845 | -0.5835366 | 5.0485056 | -0.0080710 | -0.0672890 | 0.0511471 | 0.8551105 | 0.4727115 | 1.2375095 | 2.205356 | 1.294643 | 3.116068 | 16.759312 | 0.7753286 | 32.743295 |
| M231 | Ouachita Mixed Forest | east | 668 | 334 | 2.1019804 | -0.9710094 | 5.1749702 | 0.0647916 | 0.0080089 | 0.1215742 | 0.8038450 | 0.4763735 | 1.1313164 | 2.138543 | 1.157539 | 3.119547 | 9.611801 | 2.3182763 | 16.905326 |
| M242 | Cascade Mixed Forest | pacific | 6 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2 | 1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 290 | 145 | -0.9600294 | -3.3743152 | 1.4542563 | 0.0411591 | -0.0313898 | 0.1137080 | 0.7977675 | 0.5244435 | 1.0710914 | 3.076007 | 1.104043 | 5.047971 | 37.386987 | 13.4259193 | 61.348056 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
map2
## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot phi (effect of DeltaPDSI)
plot alpha (biomass growth compensation effect)
plot A (asymptote of forest biomass growth in Mg/ha/yr)
## Warning: Removed 21 rows containing missing values (geom_point).
plot k (stand biomass at half biomss G in Mg/ha)
## Warning: Removed 22 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass growth enhancement factor in % 2000-2021)
## region weighted.ge
## 1 entire US -0.2020562
## 2 pacific 0.0000000
## 3 east -0.2011978
## 4 interior west -0.4574107phi (effect of DeltaPDSI)
## region weighted.phi
## 1 entire US 0.003049736
## 2 pacific 0.000000000
## 3 east 0.002898228
## 4 interior west 0.022521022alpha (biomass growth compensation effect)
## region weighted.alpha
## 1 entire US 0.7358344
## 2 pacific 0.0000000
## 3 east 0.7436139
## 4 interior west 0.4365143A (asymptote of forest biomass growth in Mg/ha/yr)
## region weighted.A
## 1 entire US 6.341731
## 2 pacific 0.000000
## 3 east 6.418035
## 4 interior west 2.718719K (stand biomass at half biomss G in Mg/ha)
## region weighted.k
## 1 entire US 202.43532
## 2 pacific 0.00000
## 3 east 205.23592
## 4 interior west 45.65293Calculations - weighted averages subsetted to 15 ecoprovinces
- ecoprovince codes: 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332
ge
## region weighted.ge
## 1 entire US -0.2030548
## 2 pacific 0.0000000
## 3 east -0.2030836
## 4 interior west 0.0000000phi
## region weighted.phi
## 1 entire US 0.001858927
## 2 pacific 0.000000000
## 3 east 0.001859190
## 4 interior west 0.000000000alpha
## region weighted.alpha
## 1 entire US 0.7400673
## 2 pacific 0.0000000
## 3 east 0.7401722
## 4 interior west 0.0000000